Show all terms in a custom taxonomy with all child terms wrapped in a ul

You can take a look at the WordPress function wp_list_categories(). If you want to display all the terms within a given custom taxonomy you can for example use:

<?php 
$args = array(
  'taxonomy'     => 'my_custom_taxonomy_slug',
  'orderby'      => 'name',
  'hide_empty'   => 0,
  'title_li'     => '',
  'hierarchical' => 1,
  'walker'       => null,
);
?>
<ul class="menu">
<?php wp_list_categories( $args ); ?>
</ul>

If you need to adjust the html structure, you can use a custom walker that extends either Walker_Category or Walker.

You can read more about it here in the Codex:

http://codex.wordpress.org/Template_Tags/wp_list_categories